Quantum algorithms to solve partial differential equations in battery modelling

Kurzfassung

Mathematical models of electrochemical systems as batteries or fuel cells consist of sets of coupled nonlinear partial differential equations. We present variational quantum algorithms to simulate these systems on a quantum computer. The spacetime solution can be obtained as the ground state of a Feynman-Kitaev Hamiltonian evaluated via quantum nonlinear processing units (QNPUs) [1] or the system is encoded through feature maps and solved with Differentiable Quantum Circuits (DQC) [2]. These algorithms can be used on different scales from continuum modelling on cell level to molecular dynamics and thus bridging the gap to quantum chemistry which is another promising field of quantum computing in battery research. [1] Pool, A.J. et al, Phys. Rev. Res. 2024, 6, 033257 [2] Kyriienko, O. et al., Phys. Rev. A 2021, 103, 052416